Michele Flournoy, a former top U.S. Department of Defense official widely tipped as a possible replacement for Defense Secretary Chuck Hagel, has taken herself out of consideration for the job, according to multiple sources familiar with the circumstances.

Flournoy, co-founder and chief executive of the Center for a New American Security, wrote to the think tank's board of directors saying she would remain in her post and had asked President Barack Obama to remove her from consideration to head the Pentagon, the sources told Reuters on Tuesday.

One of the sources said Flournoy, whose youngest child is 13, had cited family reasons for her decision.

In an interview with Reuters earlier this year, Flournoy, who left the Pentagon in 2012, expressed some concern about the way the Obama administration centralized decision-making.

"There's a real choke point," Flournoy said. "There's only so much bandwidth and there's only so much they can handle at one time. So, things start to slow down."

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Flournoy would have been the first woman to head the Defense Department if she had been nominated and confirmed in the post. Her decision to drop out of the running was first reported earlier on Tuesday by Foreign Policy magazine.

Hagel announced his resignation on Monday.

Flournoy's decision leaves Ashton Carter, former deputy defense secretary, and the current deputy, Robert Work, as the top potential candidates for the job. Spokespeople for both Carter and Work declined to comment.

Foreign Policy said the White House could also look to Representative Adam Smith, the top Democrat on the House Armed Services Committee, to fill the post.

Smith's office declined comment.

Obama is not expected to announce his choice this week.

"The president is considering a number of well qualified candidates however, I don't have any personnel announcements at this time," said a senior administration official.

Haaretz.com, the online edition of Haaretz Newspaper in Israel, and analysis from Israel and the Middle East. Haaretz.com provides extensive and in-depth coverage of Israel, the Jewish World and the Middle East, including defense, diplomacy, the Arab-Israeli conflict, the peace process, Israeli politics, Jerusalem affairs, international relations, Iran, Iraq, Syria, Lebanon, the Palestinian Authority, the West Bank and the Gaza Strip, the Israeli business world and Jewish life in Israel and the Diaspora.